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污水流量序列关联维数的计算

Keywords: 污水管网,节点流量,污水流量序列,时间尺度,分形维数,关联维数

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Abstract:

为了获得污水管网非恒定流模拟精度要求的节点流量过程线,应用分形理论对污水流量序列的变化特性进行研究,并初步分析其中是否存在分形特征.首先,应用延迟时间法(G-P法)重构污水流量序列的相空间,计算关联维数;然后对北京市2个污水处理厂日进厂流量记录进行了研究.为了得到可靠的关联维数,分别研究了时间滞时τ=△t和τ=4△t2种情况.研究结果表明:①污水流量序列中存在分形特性;②τ=△t时,lnC(r,M)~lnr曲线存在明显的直线段,能够估计到饱和时的关联维数:0.49(污水厂A)和0.53(污水厂B);③τ=4△t时,lnC(r,m)~lnr曲线也存在较为明显的直线段,关联维数为0.75(污水厂A)和0.44(污水厂B);④2个污水流量序列的关联维数定量地说明污水厂流量来源较单一.

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